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This is a partial transcript of Special Report with Brit Hume, July 25, that has been edited for clarity. Click here to order the complete transcript.

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(BEGIN VIDEO CLIP)

Palestinian Prime Minister Mahmoud Abbas: For the sake of peace, and for the sake of future Palestinian (search) and Israeli (search) generations, all settlement activities must be stopped not and…now and the wall must come down.

(END VIDEO CLIP)

BRIAN WILSON, GUEST HOST: President Bush is meeting with both sides in the Middle East conflict, today, the Palestinian authority prime minister, next week the Israeli prime minister.

Here to help us sort out all issues is former Mid East envoy Dennis Ross. Ambassador Ross, thank you so much for joining us.

DENNIS ROSS, FMR. U.S. ENVOY: Thank you.

WILSON: And giving some guidance as to what's going on here. I mean this was a pretty, amazing picture when you really stop and think about it. Here is the president of the United States in the Rose Garden, saying very nice things about the leader of the Palestinians. This probably couldn't have happened even just a short time ago.

ROSS: Well, I think what it reflects is that President Bush genuinely believes that there is now a Palestinian partner in Mahmoud Abbas. He sees him as someone, as you said, who is not only a good person, but he and his colleagues in the cabinet are people who give their word and act on their word. And this is obviously a not so subtle contrast to Yasser Arafat.

So, he believes there is a Palestinian partner and he realizes that here is a man who does not have a great deal of authority within the Palestinian context today and we have got to find a way to build that up. So he is doing…he, the president is doing his part right now to try to build his stature, build his role, send a message to the Palestinians that he is someone who can deliver, send a message to the Palestinians that, with someone like this, the United States will be a very, strong participant in the peace process.

WILSON: Well, do you think it will have that impact?

ROSS: I think the key is going to continue to be what happens on the ground. If he is seen as delivering, we heard the Israelis are going to lift some additional checkpoints; they're going to withdraw from two additional cities.

What Mahmoud Abbas needs is for life to return to normal for Palestinians. For that to happen, he has to fulfill his side of the bargain. Up until now, what he has done is produce a cease-fire. So far, he's not yet really gone after the terrorist infrastructure.

What was very interesting today was that the president, in effect, was putting his arm around him, was identifying with key issues that is were important to Prime Minister Abbas. The fence, the security fence that the Israelis are putting up. They're putting it up precisely because there has been terror and violence. So the Palestinians don't want to see that go up. The president identified with that. On settlements, he said the settlement activity has to stop. He identified again with something important to the Palestinians. He talked about bringing down checkpoints.

So all of that was geared towards addressing the Palestinian needs. Interestingly enough, the president also, though, used the words the Palestinians have to "root out terror." When he says that, he's referring to what is their requirement in the Road Map, which is to dismantle the terrorist infrastructure. There cannot be a Palestinian state if the terrorist infrastructure is intact.

So far, Mahmoud Abbas has not believed that he has the authority yet internally to take on that infrastructure. But there will come a moment of truth when he'll have to do so. What he heard from the president today is there is no escaping that responsibility.

WILSON: How do you think this is going to play on the other side of that fence in Israel?

ROSS: I think the Israelis also have a stake in seeing Mahmoud Abbas succeed. They know if he doesn't succeed, they don't have a Palestinian partner. There is no peace without a Palestinian partner. There is no security without a Palestinian partner. So they have an interest in having him succeed as well.

What they don't want to have happen is that they are the ones who are called on to fulfill all obligations without Mahmoud Abbas, without the Palestinian authority doing their part. It can't be that only the Israelis take on their hard, tough constituencies. The Palestinians have to do so as well.

WILSON: As we pointed out, today was the day for Mahmoud Abbas and next week, it will be Ariel Sharon. Let's look forward to that meeting. What will happen there?

ROSS: Well, I think what you're going to see is that the prime minister of Israel is going to come and he's going to say to the president, look, I'm going to do everything I can to help ensure that Mahmoud Abbas succeeds. But one of the things that makes it difficult to succeed is that Yasser Arafat is there and subverts everything that Abbas tries to do. He countermands orders; he tries to discredit him, he tries to de-legitimatize him.

I would guess that we will see Yasser Arafat somehow suggesting that not enough was produced by this meeting as a way of suggesting that, in fact, Mahmoud Abbas is not delivering.

So I think what you're going to find on the Israeli side is a readiness to take certain steps, but also a desire to point out that nothing can really be achieved, as long as Arafat can subvert it. And also an emphasis on the fact that the Palestinians must also fulfill their side of the bargain. Which means collecting illegal weapons, dismantling terrorist infrastructure so that this processes can go forward.

WILSON: In the 20 or so seconds we have left, tell me how secure you think this process is. Could it still be boned up pretty easily?

ROSS: Absolutely. What we have right now is the cease-fire. We don't really yet have the peace process because at this point, neither side is actually taking on the types of tough decisions that will be necessary down the road.

WILSON: Ambassador Ross, always a pleasure. Thank you very much for joining us from New York. We appreciate it.

ROSS: Pleasure.

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